According to sensitivity studies, the $^{38}mathrm{K}left( p, gamma right){}^{39}mathrm{Ca}$ reaction has a significant influence on $mathrm{Ar}$, $mathrm{K}$, and $mathrm{Ca}$ production in classical novae. In order to constrain the rate of this reaction, we have performed a direct measurement of the strengths of three candidate $ell = 0$ resonances within the Gamow window, at $386 pm 10~mathrm{keV}$, $515 pm 10~mathrm{keV}$, and $689 pm 10~mathrm{keV}$. The experiment was performed in inverse kinematics using a beam of unstable $^{38}mathrm{K}$ impinged on a windowless $mathrm{H}_2$ target. The $^{39}mathrm{Ca}$ recoils and prompt $gamma$ rays from $^{38}mathrm{K}left( p, gamma right){}^{39}mathrm{Ca}$ reactions were detected in coincidence using a recoil mass separator and a BGO array, respectively. For the $689$ keV resonance, we observed a clear recoil-$gamma$ coincidence signal and extracted resonance strength and energy values of $120^{+50}_{-30}~mathrm{(stat.)}^{+20}_{-60}~mathrm{(sys.)}~mathrm{meV}$ and $679^{+2}_{-1}~mathrm{(stat.)} pm 1~mathrm{(sys.)}~mathrm{keV}$, respectively. We also performed a singles analysis, extracting a resonance strength of $120 pm 20~mathrm{(stat.)} pm 15~mathrm{(sys.)}~mathrm{meV}$, consistent with the coincidence result. For the $386$ keV and $515$ keV resonances, we extract $90%$ confidence level upper limits of $2.54$ meV and $18.4$ meV, respectively. We have established a new recommended $^{38}mathrm{K}(p, gamma){}^{39}mathrm{Ca}$ rate based on experimental information, which reduces overall uncertainties near the peak temperatures of nova burning by a factor of ${sim} 250$. Using the rate obtained in this work in model calculations of the hottest oxygen-neon novae reduces overall uncertainties on $mathrm{Ar}$, $mathrm{K}$, and $mathrm{Ca}$ synthesis to factors of $15$ or less in all cases.
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